IMAGER TECHNOLOGY AND DESIGN CONSIDERATIONS
2.1 INTRODUCTION
A geostationary weather satellite orbits at an altitude of 35,800 km. The Earth's radius is 6378.4 km. The Earth disk subtends an angle of 17.3 degrees at the satellite. For scanning purposes, the field of regard (FOR) for a full disk scan is defined as 20 degrees (N/S) x 20 degrees (W/E). A 1 km length on the Earth's surface at nadir subtends an angle of 28 urad (= 1 km/35,800 km) or 1.6 x 10^(-3) degrees.
GOES I-M weather satellites are currently under development. The GOES I imager is based on a flying-spot-scanning technique whereby, via motion of a two-axis scan mirror, the scene's resolution areas are optically imaged onto a single pixel (or a relatively small number of pixels). The GOES I instrument images five wavelength bands with resolutions ranging from 1 km to 8 km. The 8-km-resolution channel is scanned by a single detector pixel.
The GOES I pixel is illustrated in the upper left portion of the FOR in 
Figure 2-1 (Scanning the Field of Regard). The GOES I flying spot has an angular extent of 0.0128 degrees x 0.0128 degrees. There are 1562 horizontal scan lines over the FOR. The scan mirror moves horizontally at a rate of 20 degrees/sec. Therefore, a full disk image requires 1562 sec, or 26 minutes.
Imaging with detector arrays offers significant advantages over flying spot scanning. Depending on the detector material system appropriate for the desired wavelength, these arrays consist of many thousands to millions of detector pixels, along with a multiplexing and readout system. An array imager, with appropriate optics, would allow redundant arrays with a large 0.82 degree x 0.41 degree angular view. With 25 horizontal scan lines, an image can be formed in 3 minutes with a scan rate of 7.2 sec/line.
Since the scan rate is slower, the dwell time per pixel is longer, and the detectors in the array can collect more energy from the scene. This improves signal-to-noise ratio (SNR) and noise equivalent temperature difference (NEdT) performance. Of course, detector saturation must be prevented. Alternatively, the longer dwell time can allow us to shrink (improve) the resolution area somewhat and still collect sufficient energy to meet baseline SNR and NEdT requirements. The motivation for exploring an array imager is based on faster image formation and improved resolution and radiometric performance.
We begin this section by defining performance goals for an array imager and a brief review of focal plane array technology. We then examine the impacts from wavelength, resolution, and radiometric performance requirements on telescope design and focal plane array size. Tradeoffs associated with different scanning techniques are examined. Radiometric performance estimates are made for each channel. For cooling the detector array, the size of a passive radiative cooler is estimated and the state of the art in mechanical coolers is discussed. Design issues regarding spectral separation and common focal planes are considered. A preliminary instrument design is developed.
Performance goals for the proposed imager are based on documented NOAA meteorological requirements [GOESN89]. There are five channels to be imaged: one visible and four infrared (IR). Wavelengths, resolution goals, and principal applications are given in Table 2-1. Resolution goals for channels 1, 2, and 3 represent improvements by a factor of 2 over GOES I-M. Enhanced resolution, especially in channels 2 and 3, is considered very desirable in the requirements document.
For the visible channel (1), performance is specified in terms of SNR. An SNR of 3 is required at 0.5 percent albedo. Albedo is the ratio of solar energy reflected from a rough surface to that incident on it. The dynamic range for the visible channel extends up to 100 percent albedo.
For the IR channels, the upper end of the dynamic range for GOES I-M is 320 degrees K. An increase in dynamic range to 350 degrees K is desired. This would allow more detailed observation of extremes in surface temperatures and differential heating, and would improve the monitoring of forest fires, volcanic eruptions, and other hot spots on the Earth.
Radiometric performance for the IR channels is specified in terms of NEdT. NEdTs are specified at three scene temperatures: 200 degrees K, a typical cloud top temperature; 240 degrees K, a mid-level cloud temperature; and 300 degreesK for surface scenes. A matrix of desirable NEdTs is given in Table 2-2. Core requirements, specified for GOES I-M, are shown in parentheses in Table 2-2.
Numerous benefits could be gained from the improved NEdTs. These benefits relate to the following: more accurate corrections for Earth atmosphere absorption, detection of diurnal temperature fluctuations over land and shallow waters, better tracking of the Gulf Stream, determination of coastal upwelling in response to wind changes (all of the preceding from improvements at T = 300 degrees K), improved mid-tropospheric moisture estimates (240 degrees K), and cloud parameter estimates for improved indicators of severe convection intensity (200 degrees K).
Blackbody spectra and the IR channels are shown in 
Figure 2-2 (Blackbody Spectra and IR Channels). For the interested reader, Planck's radiation law is reviewed in Appendix A. A dynamic range increase from 320 degrees to 350 degrees K results in a thermal radiation increase of 169 percent for channel 2 (from 1.3 x 10^(-4) to 3.5 x 10^(-4) W/cm^(2) /um/sr). The impact from increasing dynamic range is less for the other channels. Because channel 2 lies farthest from the peak spectral wavelengths, and because it has the narrowest spectral band (d[[lambda]] = 0.2 um), it will require the longest integration time. Figure 2-2 also shows that channels 4 and 5 will have similar performance since the their radiation levels are close to each other.
For each channel and temperature, we can determine the rate at which photons are emitted per unit area (of blackbody source) per unit solid angle (subtended by the detecting aperture). This normalized emission rate is called the photon sterance and has units of photons/(sec*cm^(2)*sr). Our radiometric nomenclature is adopted from Vincent [VINCENT90]. Further discussion of this nomenclature is found in Appendix A. Photon sterance levels will be used later in our radiometric performance calculations.
For a given scene temperature, photon sterance levels for the IR channels are computed by integrating the spectral photon sterance Lq([[lambda]],T) over the channel wavelength bands ([[lambda]]1 to [[lambda]]2):
photons/(sec*cm^(2)*sr)
Photon sterance levels, are given in Table 2-3. Also shown in parentheses in Table 2-3 is the relative temperature derivative of the photon sterance 
. This derivative will come into play when characterizing the radiometric (NEdT) performance of the imager.
For the visible channel, we are interested in optical power levels in the range from 0.5 to 100 percent albedo. The required optical dynamic range is a factor of 200. The solar constant at the mean distance of the Earth from the sun is 0.1353 W/cm^(2) . Of this flux, 22.3 percent falls in the channel 1 wavelength band between 0.55 and 0.75 um. At a fractional albedo, A, the radiant sterance is 9.60 x 10^(-3) A W/(cm^(2)*sr). With A = 0.005 and 1.0, the radiant and photon sterance levels are given in Table 2-4.
There are temporal requirements for synoptic (full disk) and mesoscale (U.S. sectors) applications. The core requirement is for a full disk image within 30 minutes. Any 3000 km x 3000 km area must be imaged within five minutes, and a 1000 km x 1000 km area must be imaged within 2 minutes. For an array imager, these temporal requirements are very liberal. Our temporal goal is for a full disk image within 3 minutes.
2.3 FOCAL PLANE ARRAY (FPA) TECHNOLOGY
Silicon image sensor arrays are appropriate for the wavelength band of channel 1. Silicon devices respond out to 1 um. Silicon arrays have been made with up to 4096 x 4096 pixels (e.g., Loral Fairchild CCD481 or Ford Aerospace FA4096S). Pixel sizes range from 6.8 um on edge (e.g., Kodak KAF 1400 image sensor) to more than 30 um square.
Silicon image sensor arrays employ either charge-coupled device (CCD) or charge-injection device (CID) technology. In a CCD, each photoelement has a capacitor for accumulating and storing optically generated electrons. A clocking operation shifts the charges sequentially across the capacitors. The efficiency of charge transfer can be 99.999 percent. The charges appear at an output gate at the edge of the device. In a CID, the charge under each photoelement is measured, and there is no shifting of charge. Since the charges remain stationary, a selective or random readout of individual pixels is possible. The CIDs are resistant to blooming (charge spillover from an overexposed pixel to neighboring pixels) and smearing (transfer of the overexposure effect along the array).
Image sensor array architectures may be full-frame, frame-transfer, interline, or time delay and integration:
* With the full-frame architecture, rows of scene information (pixel charges) are shifted in parallel to a serial shift register, which subsequently shifts the row of information to the output as a serial stream of data. The process repeats until all the rows are transferred off the array.
* In a frame-transfer architecture, there is a parallel storage array that is not light sensitive. The captured scene from the photosensitive array is rapidly transferred to the storage array. Readout from the storage array is then performed as for the full-frame architecture while the photosensitive array is integrating the next frame.
* In an interline architecture, the photodetecting and readout functions are separated by forming isolated photosensitive regions between lines of nonsensitive (or light-shielded) parallel readout CCDs. After a scene has been integrated, the signal collected in every pixel is transferred, all at once, into the light-shielded parallel CCD.
* Time delay and integration is a mode of processing the signal charge from the detector array that enables the integration of charge from multiple detector elements. Multiple pixel-sized images of an object are added to obtain an enhanced SNR. TDI is discussed further in connection with scene scanning tradeoffs.
There are several detector material systems for IR detection. The cutoff wavelength [[lambda]]c, where the spectral response on the long wavelength side is at 50 percent of peak, depends on the temperature of the detector. Table 2-5, from [Norton91], shows the cutoff wavelength for several material systems at various detector temperatures.
A temperature of 190 degrees K can be achieved with a four-stage thermoelectric (TE) cooler. A temperature of 80 degreesK requires liquid nitrogen, a Joule-Thompson cryostat, or a single-stage mechanical cooler. Temperatures between 1.5 degrees K and 60 degrees K require multiple-stage mechanical coolers, or liquid neon, hydrogen, or helium.
Indium antimonide (InSb), platinum silicide (PtSi), and mercury cadmium telluride (HgCdTe) are all candidates for the wavelength range of channel 2 (3.8-4.0 um), but only HgCdTe is possible for the longer-wavelength channels. The relative concentrations of HgTe molecules with CdTe molecules can be adjusted in the growth process to form Hg1 - xCdxTe and obtain a desired cutoff wavelength, larger x resulting in shorter [[lambda]]c. Typical uncertainties in production of long-wavelength Hg1 - xCdxTe arrays are dx ~ +/- 0.2 percent, corresponding to a cutoff wavelength uncertainty of d[[lambda]]c ~ 0.5 um.
In a photovoltaic (PV) detector, there is a p-n junction. Photoelectrons created near the junction are separated by the junction and produce a voltage in proportion to the incident number of photons. With photoconductive (PC) detectors, incident photons are absorbed and produce free charge carriers. The carriers increase the electrical conductivity of the element and therefore decrease its resistivity. A bias circuit must be used with PC detectors. Advantages of PV over PC detectors include a better theoretical limit to the SNR, no biasing and therefore low power dissipation on the focal plane, high impedance for matching into a silicon CCD, and more accurately predictable responsivity ([Vincent90] and [Walter86]). PC HgCdTe technology is presently limited to linear arrays. So-called first-generation IR focal plane arrays were photoconductive and had a pair of electrical leads for every pixel; no multiplexing was involved. Second-generation PV arrays multiplex pixel signals to output ports on the readout integrated circuit (ROIC).
For IR imaging, PtSi offers the largest array sizes. Two-dimensional PtSi arrays have been made with 480 x 640 elements. EG&G is currently developing a monolithic-structure 512 x 512 PtSi array for the U.S. Air Force. Both monolithic (photodetection and readout on same substrate) and hybrid (PtSi photodetection silicon readout) arrays have been fabricated. As compared with other IR detectors, PtSi offers the advantages of large formats and excellent uniformity of response from pixel to pixel. However, the quantum efficiency of PtSi is very low--in the range of 0.1 to 1 percent. Quantum efficiency is the number of electrons generated per incident photon. Low quantum efficiencies require long integration times for low level incident radiation.
There is continuing debate in the industry on tradeoffs for selection of InSb versus HgCdTe for channel 2. The arguments center on detectivity, detector temperature, cutoff, cost, and uniformity. Some of this debate is reviewed by DeWames [DeWames92]. The detectivity of InSb is much better at 65 degrees K than at 80 degrees K; its performance is very poor above 80 degrees K. At 65 degrees K, InSb offers better (precorrected) uniformity and operability than HgCdTe. Operability is a term used to characterize the percent of pixels with detectivity and quantum efficiency greater than some acceptable level. An argument in favor of HgCdTe is that the cutoff wavelength of InSb cannot be tailored to the channel 2 application, whereas the chemistry of HgCdTe can tailor the cutoff to around 4.3 um. This would reduce noise and allow operating margin. Large array size and cost favor InSb technology. InSb arrays of 256 x 256 pixels have been produced, and those of 512 x 512 are in development. HgCdTe array sizes of 128 x 128 are common.
As we will see later, pixel-to-pixel uniformity is an important aspect for an imager using FPAs. Pixel-to-pixel nonuniformity is usually characterized in terms of the standard deviation of responsivity over the pixels of the array. 
Figure 2-3 (Responsivity Nonuniformity of IR Sensor Arrays) [Norton91] shows response nonuniformity of IR detector material systems. PtSi is seen to approach a nonuniformity of 0.1 percent, whereas HgCdTe nonuniformity can be as high as 10 percent. InSb's nonuniformity falls in the 0.7 to 2 percent range. To reduce the effects of responsivity variations, an array must be characterized pixel-by-pixel. Correction coefficients are determined and gain values for each pixel are stored. However, even after this correction process, there are still residual variations. The residual variations result from pixel response nonlinearities. Residual variations have been reported as low as 0.01 percent.
The imager requires a telescope to collect and focus energy from the Earth scene. Our study of an array imager begins with telescope considerations. 
Figure 2-4 (System Considerations) illustrates the flow of imager requirements and interaction among system aspects. The wavelength requirements impact the telescope type and aperture size through considerations of chromatic dispersion and diffraction limitations. Aperture size is also driven by radiometric performance requirements. In addition to wavelength, resolution requirements enter into determining aperture size. In the telescope design, resolution requirements set an upper limit on aberrations. This establishes the telescope's field of view (FOV), which in turn determines the maximum array sizes for the channels. Dimensions of the detector array pixels, along with resolution requirements, determine the required system focal lengths. Scan techniques are driven by temporal and radiometric performance requirements, and interact with array sizes.
Telescopes fall into the categories of reflective, refractive, and catadioptric designs. Because of the wide wavelength range required for the imager (0.55-12.5 um), a common refractive telescope cannot be considered; chromatic aberrations would be too great. Some catadioptric telescopes, such as the Mangin mirror, Bouwers-Maksutov, and Schmidt systems, use mirrors with a refracting element to correct for spherical aberrations. Once again, the refractive element would result in severe chromatic distortion over the wide wavelength range. Other catadioptric designs use a shaped refractive meniscus to reduce chromatic aberration; however, the resulting focal plane is a curved surface.
The imager's wide wavelength requirements lead us to reflective telescope designs. The most common of the reflective designs are the two-mirror telescopes. These include the classical Cassegrain and Ritchey-Chrétien (RC) designs. In these two-mirror systems, the secondary mirror presents an obscuration to the collection of light by the primary. For our analysis, we assume a linear obscuration of [[epsilon]] = 0.25 (0.0625 by area).
If an angular resolution [[theta]] is to be met with an obscured aperture, then the minimum diameter D, determined from diffraction limitations, is:
,
where x is a root of J1(x) - [[epsilon]]J1([[epsilon]]x) = 0, and J1(x) is an ordinary Bessel function.
For [[epsilon]] = 0.25, we found that x = 3.59, and the diffraction law becomes:
.
Diffraction-limited apertures for the five imager channels are given in Table 2-6. Channel 5 requires the largest aperture, and we henceforth assume a telescope with a 30 cm diameter aperture. Presenting an [[epsilon]] = 0.25 obscuration, the diameter, of the secondary mirror is 7.5 cm.
We see from Table 2-6 that the diffraction-limited aperture for channel 1 is 12.3 cm for an enhanced resolution of 14 urad (0.5 km). However, if we accept the standard 28 urad (1 km) resolution, the minimum diameter is 6.1 cm. Since this diameter is smaller than the 7.5 cm obscuration of the 30 cm telescope, it allows for an interesting design of a two-telescope imager; a 30-cm reflective telescope for the IR channels and a 7.5 cm refractive telescope for the visible channel, positioned within the obscuration of the IR telescope. This design concept is illustrated in 
Figure 2-5 (Two-Telescope Imager). Time did not allow us to pursue the two-telescope design, but we mention it here as a design alternative to the single-telescope system, which we analyze in detail.
Aberrations distort the focused image in a telescope. Aberrations include spherical, coma, astigmatism, and Petzval curvature. The Cassegrain telescope, with paraboloidal primary and hyperboloidal secondary mirrors, corrects for spherical aberration. The RC design has aspheric surfaces chosen to correct for both spherical and coma aberrations. Both designs have been built and flown in space. The visible and infrared spin scan radiometer (VISSR) and Hubble telescopes are RC designs. Since the RC corrects for more aberrations, and since we desire the largest FOV, we analyze the RC design.
The RC telescope suffers from astigmatism and Petzval field curvature. Aberrations are a function of the f/# of the primary mirror; the lower the f/#, the worse the aberrations. However, lower primary mirror f/numbers are desirable because mirror spacings are closer, the telescope is more compact, and there is more working distance behind the primary mirror before the beam comes to focus. Extra working distance for the aft optics (beamsplitters, filters, lenses, stops, etc.) is important since there are five channels to process.
The maximum full FOV is defined as twice the angle at which aberrations result in a spot diameter equal to the required instantaneous field of view (IFOV). Astigmatism and Petzval aberrations were computed for the RC telescope according to [Wolfe89]. The magnitudes of the aberrations were added to determine a blur radius. The blur diameter divided by the focal length is the blur angle. The blur angle increases with the off-axis angle of incidence. The off-axis incidence angle was increased, and the blur angle was allowed to increase up to the IFOV for each channel. The analysis was performed as a function of primary mirror f/#. The results of this analysis are shown in 
Figure 2-6 (Field of View for 30 cm f/12 Ritchey-Chrétien Telescope). For an f/1.4 primary, the 14 urad IFOV of channel 1 limits the maximum FOV to approximately 0.42 degrees. A 28 urad IFOV, corresponding to 1 km resolution, allows a 0.59 degree FOV. The 56 urad IFOV of channel 2 allows a 0.84 degree FOV, and channels 3-5, with 112 urad resolution, allow a 1.18 degree FOV.
Channel 1 restricts the telescope FOV. Further analysis of RC telescope aberrations shows that the dominant aberration is Petzval field curvature. In effect, the focal plane is curved. A field corrector lens may be used to reduce Petzval aberration, and it is not unreasonable to assume that the correction will double the FOV from 0.42 degrees to 0.84 degrees. The field corrector lens would be required only for the optics of channel 1, not the other channels.
A square array has N x N pixels. The required FOV for an N x N array is N(IFOV)[[radical]]2. The factor [[radical]]2 increases the diameter of the circular FOV so that it encompasses a square array (i.e., the array diagonal is the diameter of the telescope's FOV). In 
Figure 2-7 (Field of View and Array Size), FOV is plotted against array size for the three resolutions.
For channel-to-channel coregistration, all channels must have a common FOV. The 0.84[[ring]] FOV of the 30 cm f/12 RC telescope, indicated by a dark line in Figure 2-7, falls between two sets of array sizes. The optimistic set consists of a 1024 x 1024 array for channel 1, a 256 x 256 array for channel 2, and 128 x 128 arrays for channels 3-5. The optimistic set would require a telescope FOV of 1.16 degrees. The pessimistic family of array sizes is 512 x 512 for channel 1, 128 x 128 for channel 2, and 64 x 64 for channels 3-5. In our aberration analysis of the RC telescope, we added the magnitudes of the astigmatism and Petzval contributions. This is known to be a worst-case situation, so there is some justification for optimism. Furthermore, preliminary results of ray tracing analyses on an optimized RC telescope are encouraging. We are optimistic.
Redundancy is desired in spacecraft systems to avoid single points of failure. In our array size arguments, we assumed a square array. However, for redundancy, we will place two identical arrays within the FOV. Redundant rectangular arrays are illustrated in 
Figure 2-8 (Redundant Arrays in the Field of View). Redundancy reduces the array width by a factor of 2. The optimistic family of redundant array sizes is 1024 x 512 for channel 1, 256 x 128 for channel 2, and 128 x 64 for channels 3-5.
We assume square pixels in the array. For a channel 1 silicon array, we assume a 15 um pixel edge. For InSb (channel 2), we assume 30 um, and for HgCdTe (channels 3, 4, 5), 40 um. These dimensions are typical of commercial products. The corresponding physical dimensions of the optimistic array family are 15.4 x 7.7 mm (channel 1), 7.7 x 3.8 mm (channel 2), and 5.1 x 2.6 mm (channels 3-5).
2.5 SCANNING
Before discussing scanning techniques, we need to distinguish between scene pixels and detector pixels. Scene pixels are characteristic of the object (the Earth) and are characterized by the nadir resolution or equivalent angle (IFOV). For the visible channel, the entire 20 degree x 20 degree field of regard (FOR) is divided into 6.2 x 10^(8) scene pixels. Each of these scene pixels represents an angular IFOV of (14 urad)^(2) , corresponding to an area of (0.5 km)^(2) at the subsatellite point (nadir). The detector array comprises a number of detector pixels. A detector pixel is a very small square area of detector material, measuring (15 um)^(2) in the case of the visible channel. The system optics image scene pixels onto detector pixels in the focal plane.
Two methods of scanning are addressed: step-stare and time delay and integration (TDI). We first address the step-stare scan technique. The 20 degree x 20 degree FOR is to be scanned in 3 minutes. With the optimistic array set, all five arrays see the same 0.82 degree x 0.41 degree FOV. There are 1190 FOVs in the FOR. To accomplish a 180 sec scan, the FOV may dwell up to 180/1190 = 151 milliseconds (msec). We will see later that this time interval is very long in comparison with maximum integration (exposure) times for detector arrays.
In a step-stare scan, it is desirable to overlap the FOV steps. Overlap allows consecutive FOV registration and partially compensates for any dead pixels in the detector array. Dead pixels are programmed out of the final sum. Consider the FOV of the array oriented to view 0.82 degree in the North-South direction and 0.41 degree in the West-East direction. If we require that every scene pixel (e.g., 0.5 km x 0.5 km Earth region) be viewed by four different detector pixels and their results averaged, then the 0.82 degree x 0.41 degree FOV will advance by 0.205 degrees in a west/east scan line. After completion of a scan line, the FOV will step downward (north/south direction) by 0.41 degrees. This is equivalent to a FOV measuring 0.41 degrees x 0.205 degrees stepping through the FOR. The maximum dwell in this case is 38 msec--still relatively long compared with detector saturation exposure times. Thus, even with a four-fold FOV overlap, step-stare dwell times are not limiting.
TDI is an alternative scanning technique. To illustrate TDI, we look at 
Figure 2-9 (TDI Scanning) and suppose that the 20 degree x 20 degree FOR is divided into 25 horizontal scan lines (20 degrees/0.82 degrees ~ 25). For channel 1, we use a 1024 vertical x 128 horizontal array. This array, as well as the other coregistered arrays, scans horizontally at a rate of 2.8 degrees/sec to form a 3 minute full disk image. As the array scans horizontally, each channel 1 scene pixel is seen by 128 detector pixels. The accumulated photoelectrons from the 128 pixels are added, and the final sum is read out.
As long as the detector pixels do not fill to saturation, there is an SNR performance benefit provided by the TDI scan over the step-stare approach. Essentially, this benefit arises from the coherent linear addition of signal photoelectrons to the incoherent root mean square (rms) addition of noise electrons. If there are m pixels in TDI, the SNR is improved by a factor of [[radical]]m. Measurements have shown this improvement is valid and precise. With 128 pixels in TDI, channel 1 will have an improvement of 11.3 over the step-stare scan.
Our choice of 128 pixels in TDI for channel 1 is arbitrary. Silicon arrays have been made with 96 pixels in TDI, and 128 is not unreasonable. Figure 2-9 shows a family of TDI array sizes for all five channels. These arrays would be coregistered, simultaneously viewing the same scene area. At an angular velocity of 2.8 degrees/sec (7.2 sec/line), the maximum dwell time per detector pixel is 0.289 msec for channel 1, 1.156 msec for channel 2, and 2.312 msec for channels 3-5. Figure 2-9 shows the TDI array scanning from left to right. At the end of this scan line, the array moves to the next scan line and moves right to left, with reversal of the charge addition process. This feature is referred to as a bidirectional TDI array. Redundant TDI arrays are easily fit within the telescope's FOV since, the TDI arrays are thinner than those portrayed in Figure 2-8.
In addition to the SNR enhancement, TDI offers several other advantages over the step-stare scan. The adding/averaging process of TDI results in better pixel-to-pixel response uniformity. As will be discussed later, uniformity is very important for array imagers. Inoperable or dead pixels may be deselected in a TDI array. Furthermore, the redundancy inherent in the TDI array lessens production yield requirements, and therefore reduces development risk and cost. All focal plane vendors and sensor system developers contacted during the course of this effort were advocates of TDI. Further arguments on the TDI/step-stare tradeoff, from a navigation/registration perspective, are found elsewhere in this document.
Whether a TDI or step-stare scan is employed, we can estimate the downlink data rate from the satellite to a ground station. The data rate is found by determining the total number of scene pixels, encoding each pixel in a data word, and then transmitting the resulting data load within a specified (3 minute) interval. The total number of scene pixels is1 6.9 x 10^(8) . Later, we will see that radiometric goals require encoding with 11 bits/pixel, and on top of this we allow a 20 percent overhead. The resulting data load is 9.1 x 10^(9) bits (b). If this data load is sent within 3 minutes, the data rate is on the order of 50 megabits per second (Mbps). However, data compression could result in a reduced data rate. Therefore, with compression the downlink would require a data rate well within transponder capability that would be employed on a nondedicated communications satellite.
The dwell times determined in the previous section are an upper bound on detector integration times. The integration time is determined by the upper end of the instrument's dynamic range, and detector characteristics such as quantum efficiency and electron well capacity. These parameters depend on the detector material system, pixel size, and maximum radiation level from the scene. Integration times will vary considerably over the five channels.
Maximum IR radiation levels are at a scene temperature of 350 degrees K. Table 2-3 provides the 350 degrees K photon sterance levels, 
. The resolution areas, Ares, of the blackbody sources are (2 km)^(2) for channel 2 and (4 km)^(2) for channels 3-5. The 30 cm optical aperture of the telescope subtends a solid angle of [[Omega]] = 5.5 x 10^(-17) sr, and we assume that the transmission of the optical system (fore and aft optics) is [[tau]] = 0.25. The integration time is often defined as the time to fill the electron well to half capacity (0.5w). This leaves a little reserve to prevent the possibility of saturation. The integration time is:
.
The quantum efficiency of the detector is [[eta]] . We use [[eta]] = 0.55 for both InSb and HgCdTe, but [[eta]] = 0.0042 for the PtSi channel 2 alternative. Well capacities, taken from the technical literature on commercial array products, are w = 1.6 x 10^(7) e- for InSb, 4.0 x 10^(7) e- for HgCdTe, and 1.7 x 10^(5) e- for PtSi.
The integration times work out to 19 msec for channel 2 with InSb, 0.5 msec for channel 3, and 0.165 msec for channels 4 and 5. If PtSi were used for channel 2, the integration time would increase to 26 msec. Clearly, channel 2 paces the system because of its longer integration time. The other channels must be shuttered or attenuated to balance the integration times.
The integration times all fall well within the maximum dwell times for the overlapping step-stare scan with optimistic array sizes. However, for the TDI scan, we previously found that the maximum dwell times per detector pixel were 1.16 msec for channel 2, and 2.32 msec for channels 3-5. The implication is that with a 3 minute TDI scan, the integration time of channel 2 will be limited by the mechanics of the scan. This may be offset by the SNR enhancement provided by TDI. The impact on channel 2's radiometric performance from this limited integration time is examined later.
The per pixel integration time for the visible channel 1 is based on the characteristics of a commercially available 1024 x 96 TDI array. In this array, the TDI process works on the bucket brigade principle. Each pixel in TDI accepts the accumulated charge from the previous pixels and adds to this charge during its own integration time. The charge is then passed along to the next pixel. The specified saturation exposure pertains to the total integration time (i.e., the sum of all the TDI exposures).
The saturation exposure for channel 1 is determined at 100 percent albedo, which is 9.60 x 10^(-3) W/(cm^(2)*sr) (see Table 2-4). With the previous assumptions for solid angle, transmission, and with a resolution area of (0.5 km)^(2), the maximum incident optical power level is 330 pW. The channel 1 integration time is determined from the specified saturation exposure and pixel area as:
.
This per pixel integration time is for each of the 96 pixels in TDI. The total time for all 96 integrations is 470 usec. Scaling the integration time to our case of 128 pixels in TDI, the channel 1 per pixel integration time is tint = 3.7 usec.
Except for channel 2, the mechanical dwell times exceed the pixel integration times. To avoid saturation of the other channels, they may be attenuated to balance the exposures. An appropriate attenuation factor is found from the ratio of integration time to dwell time. Attenuation factors for exposure balancing are given in Table 2-7. With exposure balancing, all detectors integrate for their full mechanical TDI dwell time. For all channels, the total TDI integration time is 37 msec (= 128 x 289 usec = 32 x 1156 usec = 16 x 2312 usec).
At 0.5 percent albedo, the optical power collected by the telescope aperture for channel 1 is 6.4 pW. With an aft optics transmission of [[tau]]o = 0.25 and a neutral density filter with [[tau]]nd = 0.013 for exposure balancing, the detector collects Pmin = 21 nW. With 128 pixels in TDI, the SNR is:
,
where the responsivity is 400 V*cm^(2)/uJ, and the specified rms noise voltage is Vnoise = 0.2 mV. A SNR of 1200 at 0.5 percent albedo greatly exceeds the required value.
For IR photon detectors, a well-known figure of merit is the detectivity, D* . D* is the reciprocal of the detector's noise equivalent power. It is used in determining the detector's NEdT performance. There is a theoretical limit to D* based on the detector's cutoff wavelength, [[lambda]]c and quantum efficiency, [[eta]], and the background photon flux, Q, seen by the detector. For a photovoltaic detector, the theoretical limit is:
,
where [[lambda]]c is in microns, and Q is in photons/(sec*cm^(2)). This is called the background-limited (BLIP) D*. Depending on the cutoff wavelength and detector temperature, state-of-the-art IR detectors can approach the theoretical limit to D*.
The smaller the background flux Q, the better the detectivity. For our application, Q is limited spectrally by channel bandpass filters. Additionally, Q can be limited spatially with a cold shield or cold stop. The cold shield, specified by its f/# or cone angle, prevents radiation from IR sources at angles greater than the cone angle. For our computations, we use an f/2 cold shield. The cold cone has a 29 degree full angle and reduces background flux by a factor of 16, thereby improving D* by a factor of 4.
Theoretical D* values were computed for each material system ([[eta]] = 0.55 for InSb and HgCdTe; [[eta]] = 0.0042 for PtSi) and each channel at the scene temperatures of interest. The resulting BLIP D*s are given in Table 2-8.
Several FPA vendors claimed that for the lower-wavelength channels (2 and 3), a 50 percent BLIP D* could be expected; however, for the longer-wavelength channels (4 and 5) only 10 percent BLIP could be expected. We followed their suggestions for the computation of NEdT performance. NEdT can be evaluated in terms of system parameters as:
.
Table 2-9 shows NEdTs computed for the step-stare scan with 50 percent BLIP detection assumed for channels 3 and 4, and 10 percent BLIP for channels 4 and 5. Values in parentheses do not meet the GOES N desired NEdT performance levels of Table 2-2; the majority of cases fall in this category.
Improvements in NEdT performance are attained with TDI scanning. The improvement reduces the NEdT by a factor of [[radical]]m, where m = 32 for channel 2, and m = 16 for channels 3-5. NEdTs for a TDI scan are shown in Table 2-10. It is important to note that we have not assumed bucket-brigade-style charge-passing pixels as we did for the visible channel. Rather, we have assumed here that the charge is removed from each pixel after it is exposed. The charges are then added in a higher electron-well capacity CCD. This assumption means that the per pixel integration time for TDI is the same as the step-stare integration time tint. The total TDI integration time is therefore mtint. This assumption allows us to divide the step-stare NEdT values by [[radical]]m without worrying about overexposure.2 We discussed this assumption with array developers, they considered it to be a reasonable assumption.
The TDI calculations show that all desired NEdT performance goals are met or exceeded except for the case of using a PtSi detector array. Its low quantum efficiency and detectivity result in very poor performance. PtSi is therefore considered no further.
The NEdT calculations were performed under the tacit assumption of perfect response uniformity from pixel to pixel in the array. Of course, nothing is perfect, and there will be some level of nonuniformity. Nonuniformities take the form of variations in quantum efficiency from pixel to pixel, response nonlinearities, and variations in offset (response under conditions of no light). In attempting to measure small temperature differences over the array, response nonuniformities will appear as noise. Characterization and correction of the array and frequent calibration will help. However, there will still be residual nonuniformity. Our next step is to determine a bound for residual nonuniformity. This bound depends on the NEdT.
The inverse Planck function is used in ground processing to determine the temperature from the estimated number of photons collected by the imager from the scene resolution area.
Figure 2-10 (Temperature Resolution) shows the inverse Planck function for channel 5 around 300 degrees K. The abscissa is the number of photons, P, collected during the 165 usec integration time, and the ordinate is the corresponding temperature as determined by the inverse Planck function. The desired 0.1 degree NEdT is indicated. If residual nonuniformities result in a pixel-to-pixel variation, dP, in the estimated received number of photons, then to achieve a specified NEdT, the relative variation must be bounded by:
.
P and 
are the Plank function and its derivative. Thus the NEdT sets a bound on residual array nonuniformities. We determined the maximum residual nonuniformities for all channels and their specified scene temperatures. The results are given in Table 2-11. The most demanding requirements are imposed by channels 4 and 5 at the scene temperature of 300 degrees K. To achieve the GOES N desired 0.1 degree NEdT, a residual array nonuniformity of less than 0.1 percent is required. Experimental residual nonuniformities as low as 0.012 percent [GOESN91] have been reported. Other developers have reported TDI arrays with 0.1 percent nonuniformity. The requirement is therefore within the state of the art.
The TDI scan provides a better uniformity characteristic than the step-stare scan. By summing m pixels in TDI, the standard deviation is reduced by a factor of [[radical]]m. This further amplifies the arguments favoring the TDI scan.
Another impact levied by the NEdT requirement, along with the extended dynamic range, lies in encoding of the pixel samples. Specifically, the number of bits used to encode each sample is determined from these performance requirements. An insufficient number of bits will result in quantization noise greater than the desired NEdT. We use the worst case of channel 5 for this analysis.
At the maximum temperature of 350 degrees K, the spectral photon exitance (see Appendix A) from a blackbody at [[lambda]] = 12 um is Qmax = 3 x 10^(17) photons/(sec*cm^(2) *um). The electrical output of an ideal photodetector is proportional to the input photon flux. If there are N bits for encoding, there are 2^(N ) levels (bins) into which the detector's output is quantized. If the flux range from 0 to Qmax is divided equally into 2^(N) levels, then the flux increment dQ is:
.
With N = 10 bits for encoding (as is used in GOES I-M), the flux increment is dQ = 2.9 x 10^(14) photons/(sec*cm^(2)*um). A plot of the inverse Planck function for channel 5 in increments of dQ is given in 
Figure 2-11 (Inverse Planck Function for Channel 5). Detection of flux values in the range of 0 to dQ is in the first bin. The corresponding temperature is 116 degrees K. Any scene temperatures up to 116 degrees K are quantized to this first bin. The next dot up the curve is at T = 124.3 degrees K at twice the unit flux 2dQ. Any scene temperature between 116 degrees K and 124.3 degrees K is quantized in the second bin. The resolution rapidly improves with temperature since the inverse Planck function becomes very steep. Resolution is defined here as the difference in temperature levels separated by unit flux steps dQ.
Resolution as a function of temperature is seen in 
Figure 2-12 (Quantization Noise Resolution for Channel 5). At 200 degrees K, the resolution is 0.44 degrees, which is within the desired 0.5 degree specification. Similarly, at 240 degrees K, the resolution is 0.23 degrees, which is within the 0.3 degree specification. However, at 300 degrees K, the resolution is 0.13 degrees and is worse than the desired 0.1 degree specification. In this case, quantization noise is larger than the desired NEdT. Encoding with more than 10 bits will decrease quantization noise and improve resolution. We found that with 11 bits, the quantization noise allows a resolution of less than 0.07 degrees on a 300 degree K scene, and 12 bits are necessary to resolve better than 0.05 degrees.
2.7 DETECTOR COOLING
To approach background limited detection, the IR detector arrays must be cooled. The maximum detector temperature for BLIP operation is a function of cutoff wavelength and background flux levels: the longer the cutoff wavelength, the colder the detector must be. The cutoff wavelength for channel 5 is at 13.5 um, one micron above the upper end of its optical passband. With an f/2 cold stop, a scene at 200 degrees K gives a background flux of 5.7 x 10^(15) photons/(sec*cm^(2)). Using IR Handbook nomographs, [WOLFE89] we found the maximum detector temperature for BLIP operation to be 80-85 degrees K. However, this is a theoretical maximum, and all focal plane array developers we contacted emphasized the importance of operating at 65-70 degrees K. In addition to cooling the IR detector arrays, the cold shields and aft optics of the imager system must be cooled, though not necessarily to the temperature of the detector arrays.
A passive radiative cooler radiates heat into cold space. The ideal radiative cooler radiates a flux, Q, from its area, A, at temperature T according to Stefan-Boltzmann's law:
,
with [[sigma]] = 5.67 x 10^(-8) W/(m^(2)*K^(4)). If we estimate a minimum heat load of Q = 1 W for array dissipation and parasitic heat creeping through support structures, and require the radiative cooler surface at a temperature of T = 60[[ring]] to provide a temperature difference between the arrays and the radiator for heat to flow through a reasonably sized thermal link, then the minimum area of the radiator is found to be A = 1.4 m^(2) or 1.2 m on edge. This is a large radiator and would, in practice, probably be larger because of less-than-ideal conditions. In fact, a doubling of the radiator area might be expected in practice. This large radiating surface must be thermally isolated from the platform on which it is mounted, and shielded from sunshine and Earthshine. Shielding of such a large surface may be very difficult to achieve on a nondedicated spacecraft. We therefore turn our attention to mechanical coolers.
Two mechanical coolers that show promise of long-lifetime operation are the Stirling engine and the reverse turbo-Brayton refrigerator. Both of these refrigerators have been designed for 10-year operating lifetimes. The Stirling engine for British Aerospace was originally designed by Oxford University and Rutherford Appleton Laboratory. The Stirling cooler consists of three components: a compressor, a displacer, and electronics. The detector is cooled by thermal contact with a cold finger. This cooler can supply 0.8 W of cooling capacity at 80 degrees K with a power consumption of 35 W. The mass of the refrigerator is 8.4 kilograms (kg) (18.5 pounds). In 1992, the Stirling cooler was flying on the Improved Stratospheric and Mesospheric Sounder (ISAMS) experiment on the NASA Upper Atmosphere Research Satellite (UARS), and on the European Remote Sensing (ERS-1) Satellite. Stirling coolers are being built in the United States by TRW, Creare Inc., Hughes, Lockheed, and Ball Aerospace. TRW has developed and tested a miniature Stirling engine capable of 0.25 milliwatt (mW) cooling at 65 degrees K with a power input of 18 W.
Creare Inc. is developing a 65 degree K Stirling cooler with a 2 W capacity, with a 60 W input power and a target mass of 14 kg (31 pounds). The cooler is designed for a 10 year lifetime with 95 percent reliability. The Ball Aerospace Stirling cooler can provide 0.8 to 3 W of cooling capacity at 80 degrees K, with a power consumption of 60 W. Its mass is 12 kg (26.4 pounds), and is also designed for a 10 year lifetime.
The reverse turbo-Brayton refrigerator, also under development by Creare, works by compressing and expanding neon gas through tiny turbines. The compressor turbine rotates at 300,000 revolutions per minute (rpm), and the turbo-expander spins at 600,000 rpm. After the refrigerator starts and the turbines lift off, the turbine rotor is suspended on gas bearings, and there are no touching parts to wear out. The most likely failure mechanism is the three-phase motor that spins the turbines. Other factors that could affect reliability are particle jamming (e.g., impurities in the neon gas) and material mismatches. The lifetime goal is 10 years. The cooler is being designed to deliver 5 W of cooling at 65 degrees K, with a power consumption of 200 W (specific power = 40W/W). The mass of the cooler is 13.7 kg (30 pounds).
The reverse turbo-Brayton refrigerator is preferred over the Stirling engine for our imager application. One reason is that piston movements of the Stirling engine impart some level of vibration to the host spacecraft, whereas with the Brayton, virtually no vibration is imparted to the mounting structure. The second reason is that the Stirling refrigerator is basically designed to handle only a single load at the end of its cold finger. In our multiple-array application, several Stirling engines would be required, and several more when redundancy is considered. The turbo-Brayton, however, can service multiple loads at multiple locations. Our imager will have as many as four IR arrays, cold shields, and optics to be cooled, and the turbo-Brayton is best suited to this application. 
Figure 2-13 (Reverse Turbo-Brayton Refrigerator with Multiple Heat Loads) is a schematic of the components of a turbo-Brayton refrigerator, with multiple loads being cooled in parallel. The neon gas flows through 1/4" tubing. Refrigerator plumbing lines may be routed to various array and aft optics locations.
A typical lifetime design goal specification is a 95 percent chance of operation after a period of 10 years. Thus the probability of failure of a single refrigerator is p = 0.05 after 10 years of operation. With a redundant compressor, expander, and motor, the probability of failure is p^(2) = 0.0025 or 0.25 percent. A redundant compressor and expander system would be valved into the plumbing of the primary system.
Technical risk lies in the lifetime of the mechanical coolers. Design goal lifetimes may be quoted at 10 years, but there are no flight test data over this long period of time. The turbo-Brayton refrigerator is still under development. A brassboard model now exists, and an engineering development model (EDM) is to be completed by the end of the third quarter 1993. The EDM will then be subjected to laboratory testing and parametric mapping. The current development schedule calls for protoflight hardware to be constructed by early 1995. Low-rate initial production (LRIP) refrigerators, if funded, would be available in the 1996/7 time frame.
The fore optics consist of the scan mirror and telescope. The aft optics reside behind the primary mirror of the telescope. The functions of the aft optics are to separate the collected radiation into the spectral channels, prevent stray radiation by stopping and filtering the beams, and focus the beams on the focal plane detector arrays.
Approaches to spectral separation of the beam include dispersion by a prism, diffraction with a grating, and optical filtering. The benefit of spectral separation with a prism or grating is less loss than an approach using beamsplitters. Several filters (dichroic beamsplitters) in series add to the loss of the system. Another advantage of a prism/grating separation over the full IR band of interest (3.8-12.5 um) is that it would provide the hook for adding additional spectral channels desired for GOES N. With the series beamsplitter approach, adding extra channels would radically alter the optical layout and add to insertion losses. With a grating or prism, the separation is done over the full band, and it is a matter of component spacings to collect and focus the wavelengths of interest. The concept of spectral separation with a grating over the full IR band of the imager is illustrated in 
Figure 2-14 (Spectral Separation with a Grating). The concept is similar with a prism.
A recent study [GOESN91] suggests an approach that avoids beamsplitters. It describes a common extended focal plane providing enhanced channel-to-channel co-registration. However, no method is suggested as to how the beam is to be spectrally separated.
A potential problem with the grating or prism is that the passband of both channels 4 and 5 is 1 um wide, and the upper edge of channel 4 (11.2 um) is only 0.3 um from the lower edge of channel 5 (11.5 um). The diffraction (or dispersion) required to separate these channel edges and also to work over the full 3.8 um-12.5 um spectrum could result in a very complicated aft optics system, possibly more complex than that of the beamsplitter approach. The grating/prism approach needs further analysis.
Another imager instrument design issue is the use of a common FPA for multiple channels. Let us examine the radiometric performance penalty for a common array. Suppose that all four IR channels are to be detected with a common focal plane detector array. The only possible material system is HgCdTe, and the cutoff wavelength must be around 13.5 um, 1 um above the upper band edge of channel 5. The thin-line curve in 
Figure 2-15 (Detectivity Tradeoff (300 degrees K Scene, 2[[pi]] sr FOV)) shows the well-known contour for the theoretical maximum detectivity with a 300 degree K background flux. The detector FOV is 2[[pi]] sr. For a cutoff wavelength [[lambda]], the contour gives the maximum achievable D* for an HgCdTe detector ([[eta]] = 0.55). The theoretical detectivity curves for two detector arrays are shown with thick lines--one with the required 13.5 um cutoff and the other for an array with a 4.5 um cutoff.
We wish to compare the degraded performance of channel 2 detected with a 13.5-um-cutoff common array against the performance of a system with an array optimized for channel 2 (i.e., with [[lambda]]c = 4.5 um). The penalty at 4.0 um, projected with dashed lines in Figure 2-15, is a factor of 8 in detectivity. The detectivity of the optimized 4.5 um cutoff detector at 4 um is 8 x 10^(10) cm[[radical]]Hz/W, whereas if the 13.5-um-cutoff common array is used, the detectivity is 1 x 10^(10) cm[[radical]]Hz/W. Furthermore, since array developers were consistent in estimating 10 percent BLIP for long-wavelength IR detectors and 50 percent BLIP for short-wavelength IR detectors, the degradation factor is multiplied by a factor of 5. The estimated D* degradation is therefore on the order of a factor of 40. It follows that NEdT performance will suffer by a factor of 40. The feasibility of a common array for all four IR channels is therefore questionable.
In our discussions with detector array developers and imaging system houses, the possibility of using a single HgCdTe array for channels 4 and 5 was suggested. The possibility of using an InSb array for both the visible channel and the 3.8-4.0 um IR channel was also discussed. A tradeoff similar to that illustrated in Figure 2-15 may be performed on the case of combining channels 4 and 5; only a small penalty is expected. These two-channel combination cases need further analysis. Here we proceed under the assumption of four separate IR detector arrays.
We now focus on a specific optical implementation for the imager. It is a preliminary design and is not optimized. Its purpose is to identify optical parameters (lens spacings, surface curvatures, focal lengths, etc.) to a point where analysis of optical performance (e.g. spot size, transmission) can be carried out by ray-trace simulation. This analysis would be used to determine problems and optimize performance. Such analysis was beyond the resources available for this effort, but should be performed in the event of a follow-on effort. We assume a system with five FPAs, and therefore five separate optical paths.
If a detector pixel is square with an edge length h, and an IFOV is to be focused within the pixel, then the required system focal length, f, is:
,
where the system consists of the combination of fore and aft optics.
The required IFOVs and assumed pixel sizes, shown in Table 2-12, determine the necessary focal lengths for the various optical paths of the system.
The focal length of the RC telescope is fT = 360 cm. For each channel, a lens system must be placed between the telescope and the detector array. The system focal length, f, is approximated from the thin lens equation:
,
where x is the location of the principal point of the lens system measured from the focal point of the telescope. To determine the appropriate lens focal lengths, we solve this expression for fL in terms of fT and f. The required lens focal lengths are determined from:
(x, f in cm).
Telescope geometry is illustrated in 
Figure 2-16 (Telescope Geometry), and the coordinate x is shown. For the f/12, d = 30 cm, f/1.4 primary RC telescope under consideration, the telescope parameters are:
focal length fT = 360 cm
obscuration [[epsilon]] = 0.25
beam angle [[beta]] = 4.77 degrees
mirror spacing D = 31.5 cm
back focal length B = 90 cm
working distance W = 58.5 cm (behind primary, before focus).
The range of the coordinate x is up to W = 58.5 cm.
Our design uses a series of dichroic beamsplitters for spectral separation of the five channels. The diameter of the telescope beam as it just emerges behind the primary mirror is 4.88 cm. We use a series of 45 degree-oriented beamsplitters, each being the diagonal of a 6 cm x 6 cm x 6 cm cube. Our first aft optics design is illustrated in 
Figure 2-17 (First Aft Optics Design). Lens positions, beam diameters, focal lengths, and operating f/numbers are shown for each lens.
The first dichroic beamsplitter in the optics train splits the visible from the IR channels. The visible channel 1 is filtered and attenuated by an optical bandpass filter and neutral density filter (BP&NDF). The total attenuation of the BP&NDF was given in Table 2-7. The visible beam is then focused by an f/4.2, 15.1 cm lens onto the visible detector array. The beam is depolarized by a beamsplitter and corrected for the telescope's Petzval curvature by a field flattener lens.
The second beamsplitter in line separates the IR spectrum at 5 um. Channel 2 is split off, filtered and attenuated, and focused by an f/2.1, 6.56 cm lens. The FOV of the channel 2 detector array is limited by an f/2 cold shield. A Lyot stop images the entrance pupil and prevents stray light from reaching the detector array.
Channels 3, 4, and 5 are split off in sequence and then focused with f/1.32 lenses. Their cold shields have been set at f/1.2. We previously computed detectivities and NEdTs based on an f/2 cold shield; however, this optics design requires a wider-angle f/1.2 cold cone. The improvement factor at f/2 was a factor of 4, whereas with an f/1.2, we only obtain an improvement of 2.6. The net result is that the D*s and NEdTs are degraded by a factor of 1.5 from the values we computed earlier.
Notice that the focal lengths of channel 3, 4, and 5 relay lenses are short. Each beam focuses quickly after its lens. This is undesirable because these infrared beams cannot be folded, with mirrors, to a common location for cooling. Cooling would be more efficient if the detectors were in close proximity. The beamsplitter orientations could be rotated to get the detector arrays closer together. Imagine, for example, that the beamsplitters and following optics for channels 2 and 4 were rotated 90 degrees, so that the detector arrays came out of the page. Still, the short focal lengths prevent a common cold area.
A second aft optics design is illustrated in 
Figure 2-18 (Second Aft Optics Design). Here we have altered the optics of channels 4 and 5. These beams are collimated by negative lenses and then focused by a positive lens with the proper focal length. This allows long high f/number beams, which can be redirected by folding mirrors. Channels 3 and 5 are in close proximity, as are channels 2 and 4. The beams of channels 4 and 5 have f/numbers of f/16.8 and f/21.9, respectively, allowing a smaller-angle cold cones. Figure 2-18 shows an f/12 cold stop. An f/12 cold stop has a theoretical improvement factor of 24; however, in practice the factor is typically limited to less than 4.
The design of Figure 2-18 could be further modified to bring all IR arrays in close proximity. For example, a third aft optics design could collimate and refocus channels 3, 4, and 5. These beams could then be manipulated in three-dimensional space and all brought close to the focus of channel 2.
With any of these aft optics designs, a detailed ray trace simulation of the optics should be performed. In particular, the impact from the required wide FOV should be examined. A potential aberration problem in any of these designs relates to angular magnification resulting from Lagrange's optical invariant. The beam diameter at the lenses for channel 5 is on the order of b = 1.6 cm. The system demagnification is m = - 30 cm/1.6 cm = -18.75. The magnitude 18.75 is also the angular magnification. Incident angles as great as 0.6 degrees (i.e., half the FOV for an optimistic array set) will be multiplied to 11.25 degrees. These large angles could cause problems since aberrations increase as angles depart from paraxial.
In previous calculations, we made an assumption of an aft optics transmission of [[tau]] = 0.25. Let us now estimate the transmission for the design of Figure 2-18. We base this estimate on the worst case with channel 5. Not shown in Figure 2-18 are the scan mirror and the secondary mirrors of the RC telescope. Desired radiation from the Earth first reflects from the scan mirror, then from the two mirrors of the telescope. The telescope's secondary mirror presents a 6.25 percent area (25 percent linear) obscuration of the primary mirror aperture. The radiation then passes through four dichroic beamsplitters, reflects from a mirror, passes through the 11.5-12.5 um bandpass filter and two lenses, reflects from two folding mirrors, and comes to focus on the detector array.
The following terms and assumed values are defined:
rm = mirror reflectivity = 0.98
to = transmission through 6.25 percent area obscured aperture = 0.94
t1 = transmission at air/lens interface of lens = 0.90 (antireflection coatings are assumed3 
)
t2 = transmission through dichroic beamsplitter/bandpass filter = 0.8
In total, the beam passes through the obscuration, 6 mirrors, 5 dichroic beamsplitters/filters, and 4 air/lens material interfaces--16 events in total. The optical transmission of the system is then:
.
The sum of the exponents in the above expression totals 16. This 18 percent transmission is somewhat less than the 25 percent value assumed in earlier radiometric performance computations.
The optics in front of the IR detector arrays may be considered as a graybody with some emissivity, [[epsilon]]. Depending on their temperature, these optical elements (filters, lenses, mirrors) will radiate, and some amount of this radiation will find its way to the detector array and introduce noise. If these optics are cooled, the noise will be reduced.
A simplified model for estimating the required aft optics temperature is illustrated in 
Figure 2-19 (Cold Shield). The detector's FOV is limited by an f/12 cold stop. The aft optics are represented by a graybody of emissivity [[epsilon]]. We will compute the photon flux emitted from the aft optics graybody (within the f/12 cone) and compare it with the flux collected from the Earth scene.
On the detector, the noise flux from the graybody is:
(photons/sec),
where Mq is at the temperature T of the aft optics. The signal flux collected from the Earth scene is given by:
.
For a worst case, we have taken the Earth scene at 200 degrees K.
We now examine the flux ratio [[Phi]]signal/[[Phi]]noise in terms of the aft optics temperature. This is plotted in 
Figure 2-20 (Flux Ratio and Optics Temperature) for a worst-case aft optics emissivity of unity ([[epsilon]] = 1).
An operating point on this curve can be established from NEdT requirements. We define:
.
For a T = 200 degree K scene, Table 2-3 gives the ratio:
.
With a required NEdT of 0.5 degrees, a minimum flux ratio of 67 is found from:
.
In other words, for a 200 degree K scene, the signal level L is 67 times the differential signal dL corresponding to a scene temperature change of NEdT = 0.5 degrees. If the noise flux from aft optics radiation is greater than 1/67th of the signal flux level, a 0.5 degree scene temperature change will be hidden. The flux ratio must be greater than 67. This operating point is indicated in the graph of Figure 2-20. The optics temperature must be less than 190 degrees K. However, this may be too stringent since Figure 2-20 is based on the assumption of an emissivity of unity. If the emissivity of the optics were [[epsilon]] = 0.5, the flux ratio would double and the aft optics temperature would be between 200 and 225 degrees K.
2.9 Instrument weight and power
The total weight of the GOES I imager is 267 pounds. This represents the combined weight for the sensor assembly, electronics module, and power supply module. An itemized component weight breakdown for the GOES I subsystems was not available. Our best estimate for the weight of our array imager is 80 to 100 percent of the GOES I imager: 214 to 267 pounds, including the mechanical cooler. Because of the long-wavelength resolution requirement, the telescope size and the weight of the array imager will be comparable to those of the GOES I telescope. The weight of the turbo-Brayton refrigerator, discussed earlier, is 30 pounds. With redundant compressor/expander turbines and motors, the cooling system would weigh 40-45 pounds. We believe this would be heavier than the three-stage aluminum-beryllium radiative cooler used on GOES I.
Weight savings might be achieved with new mirror materials such as silicon carbide instead of the ultra low expansion (ULE) glass used on the GOES I telescope. Furthermore, weight reduction might be achieved with graphite epoxy as a lighter weight structural alternative to INVAR. Another area where weight savings might be realized is in the use of application-specific integrated circuits (ASICs) for the electronics and control modules.
Because of the mechanical cooler, the electrical power requirement for our array imager will undoubtedly exceed that of the GOES I instrument. The GOES I average power consumption is 120.5 W. The specific power of the turbo-Brayton cooler is 40 W/W. For an estimated heat load of 1-2 W to cool the detector and aft optics, an additional 40 - 80 W of power would be required. The required power estimate is therefore in the range of 160 - 200 W.
The above discussion can be summarized in the following conclusions:
* Second-generation FPA technology is the key to rapid imaging from a nondedicated satellite. We believe a rapid imager is feasible and can provide the enhanced resolution and radiometric performance sought by the National Weather Service.
* The wavelength and resolution requirements for the long-wavelength channel 5 dictate the size of the imager. Diffraction limitations require an optical aperture 30 cm in diameter.
* The wide wavelength range of the imager leads to reflective telescope designs.
* Rapid imaging with a large FPA requires a telescope with a wide FOV. Of the common two-mirror telescope designs, the RC system offers the widest FOV.
* The resolution of channel 1 limits the telescope's FOV, which in turn limits usable array sizes. We found that redundant TDI-architecture arrays of sizes 1024 x 128 (channel 1), 256 x 32 (channel 2), and 128 x 16 (channels 3-5) require an FOV of 1.16 degrees. The RC telescope cannot provide this wide FOV for channel 1 because of Petzval field curvature aberrations. A field flattener lens may be used to counter the Petzval aberrations.
* To meet the desired requirements for a 350 degree K dynamic range and 0.1 degree NEdT at 300 degreesK, 11-bit encoding is required.
* The low flux from imaging channel 2 temporally paces the system. The other channels must be attenuated to balance integration times.
* The material PtSi does not meet the desired NEdT performance level within the 3 minute scan time. There is continuing debate on the use of InSb versus HgCdTe for the 3.8-4.0 um band.
* TDI scanning offers certain advantages over step-stare scanning. These advantages include superior radiometric performance and reduced yield requirements which translate to lower production risk and cost.
* The most demanding NEdT requirement is to be able to detect a 0.1 degree temperature change in a 300 degree K scene in the wavelength bands of channels 4 and 5. This requirement puts a 0.1 percent limit on residual array nonuniformities. This level of uniformity is within the state of the art.
* The IR detector arrays should be cooled to 70 degrees K or less. The aft optics should be cooled to less than 225 degrees K.
* A passive radiative cooler will be too large for an imager on a nondedicated satellite. The reverse turbo-Brayton mechanical refrigerator is preferred over the Stirling refrigerator because of the multipoint and multiload nature of the imager. Mechanical refrigerator developments are well under way, with lifetime goals of 10 years.
* The concept of imaging all four IR channels with a single detector array would compromise NEdT performance by a factor of 40. However, combining two channels on a common array appears feasible.
* We developed a preliminary optical instrument design. This design is conservative in the sense that it uses an array per channel instead of common arrays for multiple channels, and it uses a train of beamsplitters to spectrally separate the channels instead of a single optical element (prism or grating). The design defines basic optical parameters for input to an optical ray tracing program. Ray tracing could reveal problems that would suggest design modifications. This process would be used to verify the feasibility of rapid imaging with second-generation FPA technology.
* We estimate that the weight of the imager will be in the range of 210 to 270 pounds. Weight savings, relative to the 267 pound GOES I imager, might be realized by use of ASICs for the electronics module, silicon carbide for the telescope, and graphite epoxy for structural supports. The power requirement is estimated in the range of 160 - 200 W. This is more than the 120.5 W GOES I power requirement because of our use of mechanical, rather than radiative, cooling.
We identified several areas where further analysis would be required to arrive at an optimum instrument design. Time and resources prevented us from delving into the following areas:
* A two-telescope design with a refractive telescope for the visible channel residing in the obscuration of a reflective IR telescope. The field-of-view constraint could be reduced, and larger arrays (faster imaging) might be possible. The resolution of the visible channel would be 1 km.
* Ray tracing, discussed earlier, to verify the feasibility of the optimistic versus pessimistic families of array sizes. Aberrations of the total system would be modeled.
* The issue of calibrating the detector arrays, which we did not examine in our preliminary design. Calibration at two or more temperatures would be required to meet the desired radiometric performance.
* Performance tradeoffs of InSb versus HgCdTe for the channel 2 array.
* Spectral separation with a grating or prism instead of beamsplitters. Using diffraction/dispersion to spectrally separate the channels offers the potential advantage of superior channel-to-channel coregistration. It also provides the hook for adding additional spectral channels.
* Combining channels on a common FPA, for example, combining channels 1 and 2 on a single InSb array, and combining channels 4 and 5 on a single HgCdTe array. Coregistration benefits may result.
2 To alleviate the well capacity saturation problem in bucket-brigade TDI, one array developer suggested the possibility of grading the well capacities so that they become progressively larger in the direction of the bucket brigade. However, there may be a problem with graded well capacities in a bidirectional TDI array, where the brigade must pass electrons in both directions.
3 Note that antireflection coating of germanium lenses is very important. For a wavelength of 12 um, the index of refraction of germanium is n = 4. Transmission at an air/material interface at normal incidence is:
t=1-[(n-1)/(n+1)]^(2).
For an uncoated air/germanium interface, the transmission is only 0.64. This would reduce the system transmission to [[tau]] = 0.046.
Table 2-1. Imager Resolution Goals
Ch. Spectral Range Spatial/Angular Resolution Applications
1 0.55-0.75 um 0.5 km/14 urad Weather monitoring, severe storm detection, cloud mapping, snow cover2 3.8-4.0 um 2 km/56 urad Nighttime cloud detection,
water vapor estimates
3 6.5-7.0 um 4 km/112 urad Jet stream location,
mid-tropospheric circulations
4 10.2-11.2 um 4 km/112 urad Surveillance of convective storms, low-level moisture, surface temperatures, winds, soil moisture
5 11.5-12.5 um 4 km/112 urad Low-level water vapor,
surface temperature
Table 2-2. Desired (and GOES I-M) NEdT Performance Goals
Ch. 200 degrees K 240 degrees K 300 degrees K Cloud Tops Mid-level Cloud Surface
2 -- < 1.00 degrees 0.1 degrees (1.4 degrees)3 0.7 degrees 0.3 degrees -- (1.0 degrees)
4 0.5 degrees 0.3 degrees 0.1 degrees
(1.4 degrees) (0.35 degrees) 5 0.5 degrees 0.3 degrees 0.1 degrees (0.35 degrees)
Table 2-3. Photon Sterance Levels (photons/(sec*cm^(2)*sr)) and Relative Temperature Derivatives (K^(-1)) for the IR Channels
Ch. T = 200 degrees K 240 degrees K 300 degrees K 350 degrees K
2 -- 1.11 x 10^(13) 2.39 x 10^(14) 1.38 x 10^(15) (0.064) (0.041) (0.030)3 3.42 x 10^(14) 2.02 x 10^(15) 3.28 x 10^(16) -- (0.053) (0.037) (0.017)
4 5.50 x 10^(15) 1.69 x 10^(16) 5.22 x 10^(16) 1.00 x 10^(17) (0.034) (0.023) (0.015) (0.011)
5 7.21 x 10^(15) 1.97 x 10^(16) 5.41 x 10^(16) 9.71 x 10^(16) (0.030) (0.021) (0.014) (0.010)
Table 2-4. Radiant and Photon Sterance Levels for Channel 1
Percent Albedo Radiant Sterance Photon Sterance @ [[lambda]] = 0.65 um (W/(cm^(2)*sr)) (photons/(sec*cm^(2)*sr))
0.5% 4.8 x 10^(-5) 1.57 x 10^(14)100% 9.60 x 10^(-3) 3.14 x 10^(16)
Table 2-5. IR Detector Cutoff Wavelengths (um)
Detector 300 degrees K 190 degrees K 80 degrees K 60-1.5 degrees K Uncooled TE Cooled Mechanically Cooled
InSb -- 6.1 5.5 5.0
PtSi -- -- 4.8 --
PV HgCdTe 1-3 1-5 3-12 10-16
PC HgCdTe 1-11 3-11 5-25 12-25
Table 2-6. Diffraction Limited Telescope Apertures
Ch. [[lambda]] (um) [[theta]] (rad) D (cm)
1 0.75 14/28 12.3/6.12 4.0 56 16.4
3 7.0 112 14.3
4 11.2 112 22.9
5 12.5 112 25.6
Table 2-7. Integration Times, TDI Dwells, and Attenuation
Ch. Integration Time Mechanical Dwell Attenuation per Pixel (usec) per Pixel (usec) Factor
1 3.7 289 0.0132 19,000.0 (InSb)
26,000.0 (PtSi) 1156 1.0
3 500.0 2312 0.216
4 & 5 165.0 2312 0.071
Table 2-8. Background-Limited Detectivities (cm[[radical]]Hz/W) with f/2 Cold Shield
Ch. Material T = 200 degrees K 240 degrees K 300 degrees K
2 InSb or HgCdTe PtSi -- 7.1 x 10^(12) 1.5 x 10^(12) 6.2 x 10^(11) 1.3 x 10^(11)
3 HgCdTe 2.2 x 10^(12) 9.3 x 10^(11) --
4 & 5 HgCdTe 8.8 x 10^(11) 5.3 x 10^(11) 3.2 x 10^(11)
Table 2-9. NEdT with Step-Stare Scan
(50% BLIP for channels 2 and 3, 10% for 4 and 5)
Ch. Material T = 200 degrees K 240 degrees K 300 degrees K
2 InSb or HgCdTe -- (1.24 degrees) (0.416 degrees) PtSi (13.5 degrees) (4.54 degrees)
3 HgCdTe 0.14 degrees 0.08 degrees --
4 & 5 HgCdTe 0.44 degrees (0.39 degrees) (0.36 degrees)
Table 2-10. NEdT with TDI Scan
(50% BLIP for channels 2 and 3, 10% for 4 and 5)
Ch. Material T = 200 degrees K 240 degrees K 300 degrees K
2 InSb or HgCdTe -- 0.22 degrees 0.07 degrees PtSi (2.4 degrees) (0.80 degrees)
3 HgCdTe 0.03 degrees 0.02 degrees --
4 & 5 HgCdTe 0.11 degrees 0.10 degrees 0.10 degrees
Table 2-11. Maximum Array Variations (percent)
Ch. T = 200 degrees K T = 240 degrees K T = 300 degrees K
2 -- 6.4 0.43 3.7 1.1 --
4 1.7 0.7 0.1
5 1.5 0.2 0.1
Table 2-12. System Focal Lengths
Ch. IFOV (urad) Pixel Edge, h (um) System Focal Length, f (cm)
1 14 15 107.02 56 30 53.6
3-5 112 40 35.7