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Wavelength (nm)

describes the image quality at a given intensity. Due to the quantum nature of light, the number of noise electrons (temporal noise) equals the square root of the number of signal electrons. The read-out process of the imagers results in a certain number of additional noise electrons. The temporal noise is added to the read-out noise since they are statistically independent values, resulting in a total number of noise electrons to be considered for the evaluation of the signal-to-noise ratio.

The dynamic range of the instrument is the quotient of signal- and read-out noise elections the sensor sees between dark and bright scenes at the given reflection coefficient of the target scene. The maximum dynamic range is the difference between the darkest and brightest possible scene. The brightest scene is typically reflection from clouds or snow.

In order to estimate the radiometric performance of optical instruments in the mid-and long-wavelength infrared spectrum, the spectral emission of the surface of the Earth must be modeled. A blackbody with an equivalent temperature of 290 K can be used for this purpose. The atmospheric transmission as a function of the wavelength is well known for a given path orientation and atmospheric characteristics. The multiplication of the spectral radiance with the atmospheric transmission results in the upwelling radiance at the sensor. The integration of it over the selected bandwidth and the multiplication with the area of the ground pixel results in the power per solid angle. After consideration of sensor altitude and effective aperture of the receiving optics the input power at the sensor's entrance aperture can be calculated. This transforms via the optical transmission factor to the input power at detector level (usually in the picoWatt region). During the integration period a certain amount of energy is accumulated per pixel. The division of that energy by the energy of one photon gives the number of photons available per pixel which is transferred by the quantum efficiency to the available number of electrons per pixel which correspond to its output signal.

To characterize the radiometric performance of an instrument with respect to the temperature resolution, we must determine the noise-equivalent temperature difference (NEAT) for the instrument The noise equivalent temperature resolution is given by the temperature difference (at scene temperature), which generates a signal equivalent to the total noise electrons at scene temperature. The NEAT characterizes the instrument in its ability to resolve temperature variations for a given background temperature.

953 Estimating Size, Weight, and Power

We must be able to estimate the size and main characteristics of the mission pay-load before completing a detailed design. We want to be able to look at several options without necessarily designing each in depth. This section provides ways to compute data rates and estimate the overall size and key parameters. In Sec. 9.6.1, we will apply these values to the FireSat example.

We have looked in some detail at the design of specific observation payloads in Sec. 9.4. However, irrespective of the nature of the particular payload, we would like to estimate its size, weight, and power even before we have done a detailed design. To do so, we can use three basic methods:

• Analogy with existing systems

• Scaling from existing systems

• Budgeting by components

The most straightforward approach is to use an analogy with existing systems. To do this, we turn to the list of existing payloads in Table 9-13 in Sec. 9.4.3 or other pay-loads that we may be aware of which have characteristics matching the mission we have in mind. Kramer [1996] offers a very thorough list of existing sensors. We look for payloads whose performance and complexity match what we are trying to achieve and make a first estimate that our payload will have characteristics comparable to the previously designed, existing payload. While this approach is rough, it does provide a first estimate and some bounds to decide whether die approach we have in mind is reasonable.

A second approach, described in more detail below, is scaling the payload estimate from existing systems. This can provide moderately accurate estimates of reasonable accuracy if the scale of the proposed payload does not differ too greatly from current payloads. In addition, scaling provides an excellent check. Most existing payloads have been carefully designed and optimized. If our new payload is either too large or too small relative to prior ones, there should be some reason for this change in characteristics. If more detailed estimates based on detailed budgets don't scale from existing systems, we must understand why.

The most accurate process for first-order payload sizing is budgeting by components. Here we develop a list of payload components such as detectors, optics, optical bench, and electronics. We then estimate the weight, power, and number of each. This is the best and most accurate approach but may be very difficult to apply at early mission stages because we simply don't have enough initial information. Ultimately, we will size the payload with budgeting by components. We will develop budgets as outlined in Chap. 10 for each payload instrument for weight, power, and any critical payload parameters. These budgets will then help us monitor the ongoing payload development However, even with a detailed budget estimate, it is valuable to use scaling as a check on component budgeting. Again, we wish to understand whether the components scale from existing payloads and, if not, why not.

### Scaling from Existing Systems

An excellent approach for preliminary design is to adjust the parameters in Table 9-13 to match the instrument we are designing. We will scale the instruments based on aperture—a main design parameter that we can determine from preliminary mission requirements. To scale, we compute the aperture ratio, R, defined by

where A,- is the required aperture of our new instrument, and Aa is the aperture of a similar instrument (Table 9-13). We then estimate the size, weight, and power based on ratios with the selected instrument from Table 9-13, using the following:

The factor K should be 2 when R is less than 0.5, and 1 otherwise. This reflects an additional factor of 2 in weight and power for increased margin when scaling the system down by a factor of more than 2. When the system grows, the R3 term will directly add a level of margin. For instruments more than a factor of five smaller than those listed in Table 9-13, scaling becomes unreliable. We recommend assuming a mass density of 1 gm/cm3 and power density of 0.005 W/cm3 for small instruments. An example of these computations for FireSat is in Sec. 9.6.1.

### 9.5.4 Evaluate Candidate Payloads

Multi-attribute performance indices can be defined for comparing optical instruments with similar performance characteristics. For high-resolution spatial instruments three basic values describe the quality (corresponding to the information content) in the image. The three defining features are the signal-to-noise ratio at spatial frequency zero (high SNR corresponds to high information content), the MTF of an instrument at the Nyquist frequency (high MTF corresponds to high information content for sampling rates between zero and the Nyquist frequency), and the ground sample distance GSD (small GSD corresponds to high information content). We define a relative quality index (RQI) to allow straightforward quantitative comparisons with a reference instrument denoted by the suffix ref.

HOI = SNR MTF GSDref

SNR^ MTFref GSD <9"22)

This relative quality index allows the designer to trade requirements with respect to each other. For example, a higher SNR can compensate for a lower MTF at the Nyquist frequency for a given GSD. Such comparisons allow for first-order insights into the relationships between complexity, performance, and cost of candidate sensors. For example, suppose we define a reference instrument to have an SNR of 512, and an MTF of 0.5 and a GSD of 25 m. If we then compute design parameters for a particular mission, we can generate a relative quality index, or score, for our design with respect to the reference instrument For instance, if our design choices lead us to an instrument with a SNR of 705.2, a MTF of 0.47 and a GSD of 30 m, then the RQI for this system will be 108%. This index offers a straightforward method for comparing several competing sensors across three key performance measures.

### 9.5.5 Observation Payload Design Process

Table 9-15 contains the details of the design process for visible and infrared systems. We begin with basic design parameters such as the orbital height minimum observation angle and ground resolution. We then compute the quantities that describe the performance of the instrument In particular, we determine the pixel processing parameters and system data rate, the size of the optics for a given pixel size, and the radiometry of the sensor. Sample computations for the FireSat payload are given in the third column.

The data rate required for observation payloads depends on the resolution, coverage, and amplitude accuracy. With the maximum look angle, tj, spacecraft altitude, h, and cross-track pixel size, X, we have to image 2t]h / X pixels per swath line (cross-track). With the spacecraft ground-track velocity Vg and the along-track pixel size Y we have to scan Vg / Y swath lines in one second. If we quantify the intensity of each pixel by b bits (2* amplitude levels) we generate a data rate, DR, of

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